## Mathematics and Statistics Faculty and Staff Publications

#### Document Type

Book

#### Publication Date

2013

#### Abstract

The study of groupoids is meager and we have recently introduced the new notion of subset groupoids and have studied them. It is interesting to keep on record that interval groupoids have been studied by us in 2010. Further when the subsets of a loop are taken they also form only a subset groupoid and not a subset loop. Thus we do not have the concept of subset interval loop they only form a subset interval groupoid. Special elements like subset interval zero divisors, subset interval idempotents and subset interval units are studied. Concept of subset interval groupoid homomorphism is developed. It is interesting to note several nice properties are developed in this book on subset interval groupoids nearly 12 theorems are given about these subset interval groupoids to satisfy special identities. An interesting feature is we can have interval subset groupoids to enjoy special Smarandache properties. Matrix subset interval groupoids and polynomial interval subset groupoids are developed and described in this book.

#### Publisher

Educational Publisher Inc., Ohio

#### ISSN

978-1-59973-226-8

#### Language (ISO)

English

#### Keywords

subset interval groupoids, subset groupoids, groupoids, George Boole, neutrosophic logic

#### Recommended Citation

W.B. Vasantha Kandasamy & F. Smarandache. Subset Interval Groupoids. Ohio: Educational Publisher Inc., 2013.

#### Creative Commons License

This work is licensed under a Creative Commons Attribution-Share Alike 4.0 License.

#### Included in

Algebra Commons, Algebraic Geometry Commons, Analysis Commons, Applied Mathematics Commons, Logic and Foundations Commons, Number Theory Commons, Other Mathematics Commons, Set Theory Commons